A Gallup Poll asked, "What is your favorite Summer Olympics event?" Of the people asked, 27 percent said, "swimming." Here is what Gallup says about the accuracy of this poll:
The results are based on telephone interviews with a sample of 1007 national adults, aged 18 years and older. For results based on the total sample of national adults, one can say with 95 percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.
Suppose 500 people in the sample of 1007 adults were women. Gallup asked these 500 women, "What is your favorite Summer Olympic event?" Thirty-five percent said swimming was their favorite. Gallup gave a margin of error for this result. This margin of error is:
A) plus or minus 3 percentage points, just as for the overall poll.
B) less than plus or minus three points because the sample for this question is smaller.
C) greater than plus or minus three points because the sample for this question is smaller.
D) less than plus or minus three points because the population of swimming fans is smaller than the population of all adults.

Question

Quizplus · Accepted Answer

The margin of error for the sample of 500 women who were asked about their favorite Summer Olympic event is likely to be greater than plus or minus 3 percentage points because the sample for this question is smaller than the total sample of national adults. As the sample size decreases, the margin of error increases. Additionally, the margin of error for this question is likely to be larger than the margin of error for the overall poll because it is a smaller subgroup within the larger sample.

A Gallup Poll Asked, "What Is Your Favorite Summer Olympics